An extensive study of dynamical friction in dwarf galaxies: the role of stars, dark matter, halo profiles and MOND

TL;DR

The paper addresses why globular clusters in dwarf galaxies survive dynamical-friction-driven inspiral, a puzzle if the halos were cuspy or if MOND applied without modification. It develops a self-consistent two-component framework (stars plus dark matter) using King-like profiles to compute dynamical friction, showing that a cored dark-halo with a core radius around 1.5 kpc and a high central DM velocity dispersion can extend inspiral times to beyond a Hubble time, enabling GC survival in Fornax. In contrast, cuspy halos yield $t_{df}$ of a few Gyr, and MOND predicts very short friction timescales (~0.09–0.3 Gyr isolated; ~0.3–2 Gyr with external fields), making the observed GC systems problematic without additional physics. The results thus constrain dark-halo structure in dwarfs, favor cores, and challenge MOND in this context, with implications for dwarf-galaxy formation and cosmology.

Abstract

We investigate the in-spiraling timescales of globular clusters in dwarf spheroidal (dSph) and dwarf elliptical (dE) galaxies, due to dynamical friction. We address the problem of these timescales having been variously estimated in the literature as much shorter than a Hubble time. Using self-consistent two-component (dark matter and stars) models, we explore mechanisms which may yield extended dynamical friction timescales in such systems in order to explain why dwarf galaxies often show globular cluster systems. As a general rule, dark matter and stars both give a comparable contribution to the dynamical drag. By exploring various possibilities for their gravitational make-up, it is shown that these studies help constrain the parameters of the dark matter haloes in these galaxies, as well as to test alternatives to dark matter. Under the assumption of a dark haloes having a constant density core, dynamical friction timescales are naturally extended upwards of a Hubble time. Cuspy dark haloes yield timescales $\lesssim$ 4.5 Gyr, for any dark halo parameters in accordance with observations of stellar line-of-sight velocity dispersion in dwarf spheroidal galaxies. We find that under the hypothesis of MOND dynamics, due to the enhanced dynamical drag of the stars, the dynamical friction timescales would be extremely short. Taking the well-measured structural parameters of the Fornax dSph and its globular cluster system as a case study, we conclude that requiring dynamical friction timescales comparable to the Hubble time strongly favours dark haloes with a central core.

Figures (4)

• Figure 1: Logarithms of the ratios of the analytical density profiles as given in Eqs (\ref{['eq:xavierapprox']}) and (\ref{['eq:xavierapprox2']}) to exact King profiles (solid and dotted lines, respectively) with shape parameters of 2, 4, 6, 8, 10, 12, 14 and 16 (from left to right).
• Figure 2: Evolution of the radius of the globular cluster for different parameters of the model. Orbital decay if only stars or dark matter contribute to dynamical friction for ${\mathcal{R}}=7$ and $\hat{v}_{c}=20$ km s$^{-1}$ (panel a). Decay including both the stellar and dark matter components (panel b), for $({\mathcal{R}},\hat{v}_{c})=(15,20),(7,20),(7,15)$, from top to bottom. In panel (c) the dependence on the dark matter core radius is shown for $({\mathcal{R}},\hat{v}_{c})=(7,20)$ .
• Figure 3: Circular velocity for the dark halo in the mass model $\hat{r}_{\rm dm}=1.5$ kpc, ${\mathcal{R}}=7$ and $\hat{v}_{c}=15$ km s$^{-1}$.
• Figure 4: Panel (a): Temporal evolution of the radial position of a massive object of $2\times 10^{5}$ M$_{\odot}$ in MOND for different values of the mass-to-light ratio and velocity dispersions $\sigma_{\ast}=10, 12, 14$ and $15$ km s$^{-1}$ for curves A, B, C and D, respectively. Panel (b): Orbit in the $(x,y)$ plane for case A.